UPSC 2017 CDS I Math Paper

Remember: In a triangle, the line segment joining the mid-points of any two sides of the triangle is parallel to the third side and half of it.
In ΔABC P and R are the mid-points of the sides AB and AC, respectively.
∴ PR || BC
PR=

1

2

BC=BQ
Remember: In a quadrilateral, if one pair of opposite sides is parallel and equal, then it is a parallelogram.
So, quadrilateral PBQR is a parallelogram
Remember: The diagonal of a parallelogram divides it into two triangles having equal area
∴ ar(ΔBPQ) = ar(ΔPQR)
Similarly, ar(ΔCQR) = ar(ΔPQR) and ar(ΔAPR) = ar(ΔPQR)
Now, ar(ΔBPQ) + ar(ΔCQR) + ar(ΔAPR) + ar(ΔPQR) = ar(ΔABC)
∴ 4ar(ΔPQR)=5 square units
⇒ar(ΔPQR)=5/4 square uits